Problem: Express your answer as a mixed number simplified to lowest terms. $5\dfrac{1}{9}-2\dfrac{1}{6} = {?}$
Find a common denominator for the fractions: $= {5\dfrac{2}{18}}-{2\dfrac{3}{18}}$ Convert ${5\dfrac{2}{18}}$ to ${4 + \dfrac{18}{18} + \dfrac{2}{18}}$ So the problem becomes: ${4\dfrac{20}{18}}-{2\dfrac{3}{18}}$ Separate the whole numbers from the fractional parts: $= {4} + {\dfrac{20}{18}} - {2} - {\dfrac{3}{18}}$ Bring the whole numbers together and the fractions together: $= {4} - {2} + {\dfrac{20}{18}} - {\dfrac{3}{18}}$ Subtract the whole numbers: $=2 + {\dfrac{20}{18}} - {\dfrac{3}{18}}$ Subtract the fractions: $= 2+\dfrac{17}{18}$ Combine the whole and fractional parts into a mixed number: $= 2\dfrac{17}{18}$